MULTIVARIATE METHODS FOR CLUSTERED ORDINAL DATA WITH APPLICATIONS TO SURVIVAL ANALYSIS

Clustered data are the rule in many clinical specialties such as ophth almology. Methods have been developed for the treatment of clustered c ontinuous or binary outcome data. Less attention has been given to ord inal outcomes which occur frequently in ophthalmology. For example, gr ading systems of cataract and diabetic retinopathy are commonly used w here a photograph is graded by comparison with a series of reference p hotographs of increasing severity. Some commonly used methods for the analysis of ordered categorical data include the proportional odds and continuation ratio models. It is difficult, however, to incorporate c lustering effects into these models. Instead, for clusters of size two , we propose a generalization of the adjacent category model given by log [Pr(i + 1,j)/Pr(i,j)] = u(i) + (j - 1)lambda + beta'x, where Pr(i, j) denotes the probability that the right (left) eye has grade i(j), x is a vector of(person or eye-specific) covariates for the right eye, u and beta are vectors of location and covariate parameters and lambda is a clustering parameter. Based on this model, and a similar model i nterchanging the role of i and j, we derive a closed-form expression f or Pr(i,j) as a function of u, lambda, and beta and use Newton-Raphson methods to maximize the likelihood. An extension of the method allows for extra agreement along the diagonal and is then a generalization o f the agreement plus linear-by-linear association model proposed by Ag resti in the setting of no covariates. We apply these methods to a dat a set of 43 diabetic subjects from the Harvard Clinical Cataract Resea rch Center, where cortical cataract grade was the outcome. We also ext end this methodology to a survival setting, where both censored and un censored outcomes are available for individual cluster members, and on e wishes to take clustering into account. We apply the survival analys is model to a data set of 1807 children (two ears per child) in the gr eater Boston area, who were followed for the development of otitis med ia over the first year of life.